Spatial statistics deals with statistical methods in which spatial locations play an explicit role in the analysis of data. A key feature of environmental information is that each observation is related to a particular location in space. We have a finite number of spatial locations, and we are interested in dependence among those locations. Historically, Gaussian processes play a central role in modelling spatial processes, so spatial data are often modelled as a realization from a Gaussian process or a function of a Gaussian process. However, there are events, such as rain, snow, storms, hurricanes and earthquakes, where extremes are of main interest, because they can be associated to catastrophic situations. Here multivariate normal distributions are inappropriate for modelling tail behavior. The most natural way for the continuous space specification of extremes is provided by the theory of max-stable processes, which can be seen as an extreme value analogy of Gaussian processes. The analysis of spatial extreme data, an active research area, lies at the intersection of two statistical domains: extreme value theory and geostatistics. This work reviews methodologies for the statistical modeling of spatial extremes, emphasizing the pivotal role of max-stable processes in extreme environmental events. Additionally, it presents recent advancements introduced in the R software, demonstrated through an application to annual maximum rainfall data for northern Portugal.